Abstract

In the condition that the real valued function f : S ? R is a arc connected function in arc connected set S ? Rn, this
paper give the definition of generalized arc connected function. The class function is the promotion of convex function
which satisfies identified local-global extremum property. Conversely, under certain conditions. the function meeting
local-global extremum property must be one of those generalized functions. Also, the optimality sufficient condition of
minx?S f (x), s.t.g(x) ? 0 is obtained under generalized connected assumption.

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